The primary objective of this trial is to determine a safe dose of adeno-associated virus (AAV) vector delivered via needle injection to the extensor digitorum brevis to be used in subsequent trials of efficacy for limb girdle muscular dystrophy patients with one of the sarcoglycan deficiencies (a, b, g, or ?). The primary endpoint on which safety will be assessed is the development of any Grade III or higher treatment-related toxicities or two or more Grade II treatment-related toxicities. The following secondary research questions will also be evaluated in the study; assessment of the efficacy of gene transfer after vector administration, measurement of neutralizing antibodies and other cellular immune responses, and surveillance of viral shedding in various body fluids after vector administration. The study is a double-blind, placebo-controlled, ascending dose, single-arm study of recombinant AAV vectors carrying a human sarcoglycan gene (a, b, g, or ?) given as an intramuscular injection to the extensor digitorum brevis (EDB) in patients with confirmed sarcoglycan deficiency. We intend to study both males and females. Three to six patients will be treated at each dose starting with the lowest dose of 1.0 x 1011. The patients will be admitted to the hospital one day before the vector administration (Day -1), which is given on Day 1, and remain in the hospital until Day 4. Follow-up visits will be conducted on Days 8, 15, and 29. The patient will then return to the hospital on Day 43 for a muscle biopsy and safety tests, to assess the toxicity to the muscle as well as gene transfer. Additional follow-up visits will be conducted on Days 53, 85, and 120, and then every 6 months for 3 years.